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Dutch version

Standing longitudinal waves

Wind instruments and  organ pipes

 

The same type of calculations

 

An antinode is created at the mouth of the pipe!

 

Example 3

Find the frequency of the fundamental of an open organ pipe with a length of 2.0 m

at a temperature of 20 C  (speed of the sound is 343 m/s)

                                       

                                                                               

                                  





 

 

 

 

 

Open organ pipe : the open top is also an antinode

Distance from antinode to antinode A-A = ½  λf 

So  λf = (2)( 2.0) = 4.0 m

v = 343 m/s

v = ff  λf

343 = ff . 4.0

ff = 85.8 Hz

 

Example 4

Find now the frequency of the fundamental of a stopped organ pipe with the same length

 

Fundamental:     

 

                                                                                                 

 

 

 

 

 

 

 

Stopped organ pipe : the closed top created a node

length pipe  (N-A) = ¼ λ       So  λ= (4)( 2.0) = 8.0 m

v = ff  λf       343 = ff   8.0      ff= 42.9 Hz    ( 2 x lower then the ff  of an open pipe)

 

Example 5

Calculate the frequency of the second harmonic of a stopped organ pipe with the same length of 2.0 m at the same temperature of 20 C

 

 

 

                

 

 

 

 

 

 

 

 

length organ pipe = 2.0 m

 

length = ¾ λ 1     λ1= 2.67 m

f1 =  128.5 Hz